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You should format the Ubuntu partition (using a tool like fdisk or cfdisk) and install Arch in that same partition. But you can also keep Ubuntu if you do not wish to remove it. That way, you could end up with 3 options: Arch, Ubuntu and Windows 8 during boot up.

Once you install Arch Linux with a bootloader (like grub or lilo), you will get an option to boot your OS of choice during each boot up, similar to what you might be getting right now.